- Email: [email protected]
c study of the DO properties
~
Nuclear P h y s i c s B5 (1968} 693-713. North-Holland Publ. Comp., A m s t e r d a m
ANTIPROTON-PROTON (K~
+ 3y)
AND
STUDY
OF
ANNIHILATION (KK THE
+ 47r) A T D°
1.2
INTO GeV/c
PROPERTIES
C. D'ANDLAU~ A. ASTIER~ L. DOBRZYNSKI, J. SIAUD Laboratoire de Physique Nucl~aire, Collbge de France. Paris J. BARLOW, L. MONTANET, L. T A L L O N E - L A M B A R D I * CERN, Geneva, Switzerland
A. M. ADAMSON, J. DUBOC, M. G O L D B E R G Institut de Physique Nucl$aire, Paris
R. A. DONALD, D . N . EDWARDS, J . E . A . LYS ** Nuclear Physics Research Laboratories, Liverpool
Received 12 March 1968
A b s t r a c t : Experimental r e s u l t s a r e p r e s e n t e d for the five- and six-body annihilations ~p --~ KK'3~ and ~p --~ KK 4~ of 1.2 GeV/c antiprotons. Analysis of these r e sults in t e r m s of production of K*(890), p , co. ~ and D(1280) resonances is made. A detailed analysis of the quantum numbers for the D - m e s o n is given.
1. I N T R O D U C T I O N In t h i s p a p e r , w e p r e s e n t a s y s t e m a t i c a n a l y s i s of t h e f o l l o w i n g s i x - a n d f i v e - b o d y ~p a n n i h i l a t i o n s a t 1.2 G e V / c : ~p -~ K~K-'e~:~+~-~ °
(122 e v e n t s )
,
(1)
~p -~ K ~ K = e ~ + ~ -
(325 e v e n t s )
,
(2)
~p - - K ~ K - ~ ( M )
(259 e v e n t s )
,
(3)
(327 e v e n t s )
,
(4)
(539 e v e n t s )
,
(5)
.o.o
+
-
~p ~ ~ 1 ~ 1 ~ ~ ~ pp ~ K~ (M) ~+~-
o
* Now at Instituto di F i s i c a . Milan. ** Now at University of Michigan. Ann Arbor, USA.
694
C. DIANDLAU
et al.
where (M) stands for m i s s i n g p a r t i c l e s in r e a c t i o n s (3) and (5). Reaction (1) is the only abundant six-body channel o b s e r v e d for this e x p e r i m e n t : O O+ other s i x - b o d y channels, such as ~p -~ KIK17r 7r (M), and ~p --~ K~(K°)zr¢~-~r+~r- have much s m a l l e r c r o s s s e c t i o n s (see table 1). As is shown l a t e r , the observation of r e a c t i o n (1) is mainly due to the p r o d u c tion of co° -~ ~r+~r-Tr° which cannot contribute to s i x - b o d y annihilations with four c h a r g e d pions. We can t h e r e f o r e safely a s s u m e that m o s t of the events (3) a r e five-body annihilations, with 2~ ° m i s s i n g , except for a few events with an 77° or an w ° decaying via t h e i r neutral modes. In r e a c t i o n (5), we have at l e a s t one K ° and ~o m i s s i n g , but we cannot exclude that a good f r a c t i o n of these events a r e six-body annihilations with one K ° and 2~ o missing, this last final state being f a v o u r e d by the p r o d u c t i o n of w °, a s in r e a c t i o n (1). A s i m i l a r a n a l y s i s of the two-, t h r e e and f o u r - b o d y annihilations at 1.2 G e V / c is a l r e a d y published (ref. [1]). One of the most i n t e r e s t i n g r e s u l t s of this a n a l y s i s is the o b s e r v a t i o n of a new S= 0 r e s o n a n c e , the D °, a l r e a d y r e p o r t e d in refs. [2,3]. This p a p e r s u p e r s e d e s r e s u l t s p r e s e n t e d in ref. [2]: in p a r t i c u l a r , we p r e s e n t h e r e a m o r e detailed a n a l y s i s of the D - m e s o n b a s e d on its o b s e r v a t i o n in the "two-body" annihilation p r o c e s s e s : pp .... D°X ° , where X ° can be identified to co°, 7 °, pO or ~o. The r e s u l t s were obtained f r o m an a n a l y s i s of ~p annihilations involving at l e a s t one visible K~ decay. The film under study was taken in the Saclay 81 cm HBC exposed to a b e a m of 1.18 ± 0.01 G e V / c ~ f r o m the C E R N , .{ (ref. [4]). The r e s u l t s p r e s e n t e d c o r r e s p o n d to the complete film sample, that is roughly 5 events/rib. E a c h event was weighted in o r d e r to c o r r e c t for the finite probability of the K~ to d e c a y outside the visible r e g i o n of the c h a m b e r and for the p r o bability that the K~ d e c a y s within 0.2 c m f r o m the production apex. T h e s e weights were used when n e c e s s a r y in the following a n a l y s i s , p a r t i c u l a r l y f o r the calculation of the c r o s s sections, for which we have also taken o into account the neutral decay mode of the K 1 and the scanning efficiency.
2. RESONANCE
PRODUCTION
IN (KI~ + 3~) AND
(KI~ + 4~) FINAL
STATES
T h e s e five- and six-body annihilations a r e dominated by the production of K*(891), p(765) and 0)o(780). The K*(891) and c0(780) production shows up c l e a r l y on fig. 1 and 3, whilst the p(765) p r o d u c t i o n just i n t r o d u c e s a r e l a t i v e l y s m a l l distortion of the (~g) s p e c t r u m (fig. 2). In addition, the neutral (KI~) m a s s s p e c t r u m has a g e n e r a l tendency to show an enhancement for all these r e a c t i o n s around 1290 MeV. This enh a n c e m e n t shows up much m o r e c l e a r l y when the p a r t i c l e s which a r e left outside the neutral (KI(~) combination f r o m a r e s o n a n t state, such as ¢0°, p o ~?o (fig. 4, 5). It has been shown in ref. [2] that the (KI~Tr) enhancement cannot be attributed to the reflection of the r e s o n a n c e s a s s o c i a t e d to its
~p ANNIHILATION
12C
t ~
695
(o)
(c) 0
~,
o
8O
0
(.9 >,
0
d
6O
40
E
0.40 ID
0.72
1.04
ld = ( K "tr)
O
2O
:3 Z
0
0.40
1.36
1"== I / 2
0.72
1,04
MZ(K..n -)
GeV =
1.36
GeV =
3, (M O
c~
(b)
.
50 i
¢n
,ID
E
C ¢D
z
25 $
4C
.D
E_ Z
0.40
0.72
1.04
M = (K'rr)
1.36
GeV =
i
0.40
i
I
i
0.60
0.80
M = (K'n')
T==I/2
"--'I'~"I~
r~
1.00 GeV z
Fig. 1. M2(KTr) distributions for five- and six-body final states. Full lines represent phase-space curves. T (la) M2(K~) in pp ~ K~K±~T~±~ . The dashed line corresponds to production of 65% K*, 26~p and 9% D°. (325 events - 4 combinations per event). (lb) MZ(Ky) in pp --~ Kl°K~?r+~-Tr°. The dashed line takes account of a production of 40% K*, 14%p, 44% Wo and 2% D°. (327 events - 6 combinations per event). (lc) M2(K~) in pp --~ K°K~-?rT(M). The dashed line was obtained for a production of 69% K*, 13%p and 1 8 ~ D °. (259 events - 2 combinations per event). (ld) M2(K~") in ~p --~ K~>K!yT~'~'~:Y °. The dashed line corresponds to a production of 46% D°W o, 19% KK~c0- and 35% K*KyyTr. (122 events - 6 combinations per event).
p r o d u c t i o n , a n d m u s t b e i n t e r p r e t e d a s a g e n u i n e r e s o n a n c e , the D - m e s o n , with M= 1290±TMeV,
F= 30+ 5MeV.
T a b l e 1 g i v e s t h e r e s u l t s of t h e f i t s p e r f o r m e d on a11 t w o - a n d t h r e e b o d y m a s s s p e c t r a . I n t h e f i t t i n g p r o c e d u r e , we have g e n e r a t e d , by M o n t e C a r l o t e c h n i q u e s , s t a t i s t i c a l d i s t r i b u t i o n s c o r r e s p o n d i n g to the p r o d u c t i o n s of K*, p, w° , D ° a n d ( D ° X ° ) , w h e r e X ° i s f o r w °, pO, 77o. We h a v e n o t t r i e d s i m u l t a n e o u s r e s o n a n c e p r o d u c t i o n s , l i k e (K*Kp), (K*K*Tr) . . . . . ,
696
C. D ' A N D L A U et al.
Q o
I00
150
_,so=.g
901~~,_ ]
_.
,;
\i '
40
so
zo
30
E 004
O.ZO 034. 0.50 0,66
M=('rr'rr)
Tz : 0
0.04 0 2
GeV =
M=('rr'rr)
0.4
0.6
Tz : 0 , 1
0178
GeV =
Fig. 2. M2(~TT) d i s t r i b u t i o n s f o r f i v e - b o d y f i n a l s t a t e s . Full l i n e s a r e p h a s e - s p a c e curves. • -0 ± = F - F (2a) M2(?T~) m pp---* KIK ?T ~ ~ . The dashed line takes account of a production of 65%K*, 26% D, and 9~oD°. ~325 ecents - 2 combinations per event). (2b) M2(77~') in ~p --* K~.K~y ~-~.o. The dashed line takes account of a production of 40%K*, 14%p, 44%¢0 and 2% D°. (327 events - 3 combinations per event).
-> (o)
(b)
(.9 OJ
o o
50
o~ =-. 40 G J,
30
E
20
20
I0
I0
Z
020
0.36
0.52
0.68
M = (-n "+ " r r - "n" ° )
0.84 GeV =
1.00
02
0.4 M=
06
0.8
GeV =
0 0 +Fig. 3. ( a ) M 2 ( ~ + ~ - ~ o) in ~p ~ KIK17T ~" 7r0 . The full line r e p r e s e n t s the p h a s e s p a c e d i s t r i b u t i o n - t h e d a s h e d l i n e t a k e s a c c o u n t of a p r o d u c t i o n of 40% K*, 14% p, 44% co ° and 2% D ° . (327 e v e n t s ) . (b) M i s s i n g m a s s s q u a r e d s p e c t r u m in ~p ~ K~K-~=F(M). (259 e v e n t s ) . The h a s h e d h i s t o g r a m r e p r e s e n t s t h e s p e c t r u m o b t a i n e d f o r the e v e n t s s a t i s f y i n g the c u t s : 1.64 GeV 2
~p ANNIHILATION
697
(a) 30
20
~> (..9 O
O M ' (K,° K± ~r ~) O'3
0,J
2C
GeVt
(b)
D°
IE 12
8
o 4
M ' ( K ~ ° K,° "rr = )
E
GeV'
(c)
=1
z
D°
[
ac
15
" ;
I0
140
1.80
2.20
M ' ( K~° K:t: Tr :1: )
260
300
GeV'
Fig. 4. M2(KKTr ) d i s t r i b u t i o n s f o r the five body s t a t e s . Full l i n e s r e p r e s e n t p h a s e space curves. (4a) M2(K~K~-Tr +) in pp--+ Kl°K±lr~:y+?r- . The d a s h e d l i n e t a k e s a c c o u n t of a p r o d u c t i o n of 65% K*, 25% p a n d 9% D o. (325 e v e n t s - 2 c o m b i n a t i o n s p e r event). The h a t c h e d h i s t o g r a m r e p r e s e n t s the s p e c t r u m o b t a i n e d f o r the e v e n t s s a t i s f y i n g the cut M2(KK) < 1.08 GeV 2 , w h i c h is m a d e to a c c e n t u a t e the p r e s e n c e of the D o . o o" ) m • -pp --~Kl°Kllr o + - oY ~ • T h e d a s h e d h •n e t a k e s a c c o u n t of a p r o d u c t i•o n (4b) M 2 (KI°KI~ of 40% K * , 14% p, 44% 0ao and- 2% D u. (327 e v e n t s - 1 c o m b i n a t i o n p e r event). The h a t c h e d h i s t o g r a m is defined a s in 4a. (4c) M2(KI°K4-~ :F) in ~p--+ Kl°I~±~r~(M). The d a s h e d l i n e t a k e s a c c o u n t of a p r o d u c t i o n of 69% K*, 13% p and 18% D °. (259 e v e n t s - 1 c o m b i n a t i o n p e r event). The h a t c h e d h i s t o g r a m is d e f i n e d a s in 4a.
698
C. D'ANDLAU et al.
Do
125 I0
7.E 5
eNI > (D 0
~ 4
ci
2
(_9
(o)
25
,L
)
6
GeV' (b)
L
o
ww(2 > Q~
M ' ( K , ° K~'n"°)
4
--,L----
,_,.._k__
GeV'
~
(C)
I
.____~__.__,___
(KT K"Tr °)
o
GeV'
16
E 2:}
Z
12 8 4
0
(KK~')°GeV'
4 2
oi__ 1.48
1.60
IBO
2 O0
M 2 ( K , K, Tr±)
220
2.40
GeV 2
Fig. 5. D p production MZ(KK~r) s p e c t r u m in f i v e - b o d y annihilations ~p ---* (KK?r)(~rTr ) when cuts a r e applied on the r e c o i l e d dipion (Trlr) to a c c e n t u a t e the p production. F o r the n u m b e r of DO expected, see table 3. (5a) M2(K~K±TrT) in ~p ~ K~K±?r=F?r+Tr- with 0.49 < M2(?r+y-) < 0.64 GeV 2. The full line r e p r e s e n t s (KK~p) phase space. The dashed line takes into account the D ° p ° production. (hb) M2(K~K°?r °) in ~p ---* K~K°Tr°Tr+y - with 0.49 < M2(y+~r-) < 0.64 GeV 2. (5c) M 2 ( K ~ K ~ °) i n , p - - . KOi~O 1( ~ 0 )?r + 7r with 0.49 < M2(?T+~r-) .< 0.64 GeV 2. (5d) Sum of h i s t o g r a m s 5a, 5b. 5c. o o q- in ~p ---, K1KI~ o 0 + 7r-lro with 0.49 < M2(Tr-+Tr°) < 0.64 GeV 2. One does (5e) M 2 (K1K~lr) not see any D ± production, as e x p e c t e d if I(D) - 0.
~p ANNIHILATION
699
M z ( -rr+ -n-- .rr ° )
(b)
o, cjl
25 %
2,3
_O ~ O REGION : o j o',
4•
2.1
"ee
->
i
.....:...-,!
(..9 A
.i' i)"::i
1.9
°x-
1.7
-=
. . . . . .
r
.......
r . . . . . . . . .
:,-
v
~ - . - - - -,;V
-ti
. . . . . . . . . . . . .
1.5
1.3
' b '!
:; "J (O)
I.I 0
:l__ i
L
i
~
0.2
_
i
,i
0.4
2
o
•
•
2
+
-
o
~
0.8
0.6
MZ(-n-+vr--rr °) •
io~ ,
o
GeV z •
•
•
o
Fxg. 6. M (KIK_ 7r ) = f [ M (ff lr lr )] i n ~ p - - * K i K _ 7~ 7r 7T~ . Two_ points+_ p e r e v e n t . D i s t r i b u t i o n s (a) c o r r e s p o n d to the p r o j e c t i o n of p o i n t s ( p a i r (KKTr, ~ lr ~ o) with o w h e r e a s d i s t r i b u t i Q n s (b) (dashed) c o r r e s p o n d to the M 2 (y ÷lr-lr o ) n e a r e r to M 2 (CO),
projection of crosses (pair (KK~, ~+y-~o) with Mz(~+~-IT°) farther from M~(W°)).
except for (D°X°). In the fitting procedure, we take account of only the decay p r o p e r t i e s of the resonances. For the D-meson, we use the following s q u a r e d m a t r i x element: iM(D)12 = tp . B w ( D ) 12, where 1
BW(D) M~,-M~o + iMDOrDo
700
C. D'ANDLAU
MDo = 1290 MeV ,
p=
et al.
FDO = 30 MeV ,
1 1 +iaPK~ '
a is the s c a t t e r i n g length for the KK t h r e s h o l d I= 1 interaction (lal = 2.0 f), and ~ is the m o m e n t u m of the K in the KI{ c.m. s y s t e m . We introduce P to take account of the disintegration p r o p e r t i e s of the D ° . This f a c t o r r e p r o d u c e s the a c c u m u l a t i o n of events at the t h r e s h o l d of M2 (KK). The f o r m adopted h e r e f o r P supposes that the s p i n - p a r i t y of the D ° is 0-. Note that another a s s i g n m e n t (1 +, 2-) for the D ° would not change the r e s u l t s of our study. (See sect. 3). F o r the m a s s e s and widths of K*, p and w, we use the values of ref. [5]. F o r the r e a s o n s given in the introduction, we do not t r y a fit f o r r e a c O + tion (5): ~p -~ KI~ 7T (M), but limit o u r s e l v e s to qualitative s t a t e m e n t s . We have also included in table 1 the r e s u l t s obtained for the f o u r - b o d y annihilations ~p -~ K~K~Ir-~ °, since it a p p e a r s to be an i n t e r e s t i n g channel for the D ° production. A m o r e detailed a n a l y s i s of this r e a c t i o n is given in ref• [1]. The r e s u l t s p r e s e n t e d in table 1 call f o r the following r e m a r k s : (i) Reaction (I): ~p -* K ~ K ~ y ~ + ~ - ~ ° is dominated by w ° production• M o r e o v e r , a l a r g e f r a c t i o n of this w ° production is a s s o c i a t e d with D ° p r o duction, so that 46% of r e a c t i o n (I) r e d u c e s to the p r o c e s s pp - . D ° ¢0°, with D ° ~ K~I~?r¥ and co° -~ ~+~-yo. The s c a t t e r d i a g r a m (fig. 6) i l l u s t r a t e s this situation. (ii) Reaction (2): ~p ~ K~K:ey~-y+ - is dominated by K*(891) p r o d u c t i o n and, to a s m a l l e r extent, by p(765) production. As with the coo in r e a c t i o n (i) a selection on pO p r o d u c t i o n in r e a c t i o n (2) enhances the o b s e r v a t i o n of the D ° , thus giving evidence f o r the p r o c e s s : ffp ~ D°p ° , with D ° --* K~K±~ "7-and pO ._, 7T+TT- .
(iii) Reaction (3) c o n s i s t s mainly of f i v e - b o d y annihilations pp --* K ~ K ~ ° v ° with 2~ ° missing. Its a n a l y s i s is t h e r e f o r e difficult. Howe v e r , it p r o v i d e s an i n t e r e s t i n g r e s u l t on the D ° production; namely, when a selection on D ° is p e r f o r m e d , the m i s s i n g m a s s s p e c t r u m shows a tendency to a c c u m u l a t e around the ~1o m e s o n and, to a s m a l l e r extent, around the w ° (fig. 3b) leading to the p r o c e s s e s : pp ~ D%?°
with
D ° __. K ~ K ~
~p --* D°¢~°
with
D °--* K ~ I ~ ~
,
~ o _.. all n e u t r a l s , w °-~ all n e u t r a l s
The evidence of pp --* D°w ° is m a r g i n a l , but not inconsistent with the observation of ~ 56 events for the channel ~p --* D°w ° with ~o __. ~+~r-~o [ r e a c tion (1)].
~p A N N I H I L A T I O N
701
Table 1 Cross sections. Reactions . 0.±
:F ~
pp--*~ll~
Observed 0
::F
0
g ~ y ?r
KIK
f i n a l s t a t e a)
4- :F . 0
, w
21.0 ± 3.0
D ° + 7/°
0.5 ± 0.5
K* + Ky~y ~p "-* K~K±Tr%~?r ±
325 events .0.4-
~p--~lXl~
~
:F
(M)
~0.0
Op ~ h l l ~ l ~
+-
0
7r ?r
o.
±
~:
D ° + ~Y
3.2 ± 2.0
D ° +po
3.2±
51.5+ 5.0
D ° + (M)
9.2 ± 3.5 2 . 6 ± 1.1
D ° + 00°
1.7± 0.8
p + KKTr a)
9.6 ± 5.0
-±0
75 ± 9
74.0 ± 10.0 82.0 ± 5 . 0 p
:FO
2 6 . 0 + 9.0
D°P °
4 . 0 ± 2.0
K* + y (M)
abundant
DO/)O
compatible with zero
DO o
o
105 ± 10
1.5
D ° + 770
(l~ll~l~)
539 e v e n t s .
70.5 ± 4 . 0 2 8 . 4 ± 5.0
...0..0
pp ~ K ~ + ~ (M)
p p --,lXliX ~ ~
K* + K~y po + KKy
K * + KTT~ KO-O o 1KI¢O
327 e v e n t s
46 ± 6
16.0 ± 6.0
K* +K(M)
259 e v e n t s
ff t o t a l (~tb)
8.7-3.0
D ° + 0)° 122 e v e n t s
ff p a r t i a l (~tb)
186 ± 17
198 ± 15
11.2 ± 3 . 0
1632 e v e n t s
594 ± 24
~p-"~ K1K~T+~-(?T O~'O)
5 ± 2
5 events 0
0
4- -
+
-
~ p - ~ K I ( K )~ ~ ~ ~
7±3
14 e v e n t s a) T h i s f i n a l s t a t e i s e s t i m a t e d ..o.
by its reflections o
+
-
e f f e c t s on t h e o t h e r d i s t r i b u t i o n s .
o
(iv) Reaction (4) ~p-~ ~1~1 ~ ~ ~T is dominated by w° and K*(891) production. However, there is a slight indication of D ° production associated to p ° production, while no such effect is observed for the charged (KI~) combinations when a selection is performed on the charged p (fig. 5b, 5e). (v) There is no sign of D ° production in reaction (5): ~ p - Ky~+~-(M), even when a selection is performed on the pO (fig. 5c). (vi) T h e p e r c e n t a g e of s t a t i s t i c a l b a c k g r o u n d f o r e a c h of t h e s e r e a c t i o n s was found to be consistent with zero.
702
C. D'ANDLAU et al.
In a d d i t i o n to t h e s e r e m a r k s , one s h o u l d n o t i c e t h e a b s e n c e of l a r g e E ° p r o d u c t i o n in t h e s e r e a c t i o n s , in c o n t r a s t w i t h t h e s i t u a t i o n o b s e r v e d w i t h ~p a n n i h i l a t i o n s a t r e s t w h e r e t h e E ° m e s o n d o m i n a t e s m o s t of t h e f i v e body reactions. The important accumulation observed for the neutral ( K I ~ ) s p e c t r u m b e t w e e n 1350 a n d 1550 M e V c a n b e a c c o u n t e d f o r by t h e r e f l e c t i o n of K* p r o d u c t i o n , w i t h o u t a n y n e e d of E ° a n d f* p r o d u c t i o n (fig. 4). A s e l e c t i o n on l o w (KK~ m a s s e s , w h i c h i s k n o w n to e n h a n c e t h e o b s e r v a t i o n of t h e E ° in ~p a n n i h i l a t i o n s a t r e s t , d o e s not l e a d to a b e t t e r e v i d e n c e f o r E ° p r o d u c t i o n in ~p a n n i h i l a t i o n s a t 1.2 G e V / c (fig. 7). C o n c e r n i n g t h e f*, t h i s n e g a t i v e r e s u l t i s in a g r e e m e n t w i t h t h e a b s e n c e of f* in - w h e r e the w e l l known d e c a y m o d e f * - c o u l d be o b s e r v e d ( r e f . [1]). T h e (KK) s p e c t r a o b s e r v e d f o r r e a c t i o n s (1) to (4) g e n e r a l l y p e a k a t t h r e s h o l d (fig. 8) a s w i t h t h e f o u r - b o d y r e a c t i o n s ( r e f . [1] a n d f o r p p a n n i h i l a t i o n s at r e s t ( r e f . [5]). H o w e v e r in c o n t r a s t w i t h t h e i n t e r p r e t a t i o n g i v e n f o r pp a n n i h i l a t i o n s a t r e s t , one c a n n o t e x c l u d e t h a t in t h e p r e s e n t c a s e , t h i s d i s t o r t i o n of t h e (KI~ s p e c t r a i s e x c l u s i v e l y d u e to t h e p r e s e n c e of t h e D ° m e s o n , a t l e a s t f o r c e r t a i n s e t s of q u a n t u m n u m b e r s JP (D), a s we s h a l l s e e in s e c t . 3 of t h i s a r t i c l e .
-> ~'- 6 o
_.= g4
o
2
z
0 2.0
2.2
M1 (K:' K==~r ' )
2.4
GeV =
2 O + :~ . O • :F + F i g . 7. M (K1K Tr ) m ~ p - ~ K1K ~ ~ ~ when cuts a r e applied to theM2(KTl)and M2(KK) to accentuate a possible production of E ° meson. The cuts applied are:
~ p - o K.K2~-2~3 ,
K*---*KI~ 1
M2(KI~I) n e a r e r to M2(K *) = 0.79 GeV 2 0.7 GeV 2 < M2(Klnl) < 0.90 GeV 2 M2(KK.) < 1.1 GeV 2 . The curve takes account of K*, p and D production, as well as of the outs p e r f o r m e d on the reaction. There is no sign of E ° production (M2(E) = 2.04 GeV2).
~p ANNIHILATION
703
(a)
(c)
N
>,~
3
0
30
~
20
2O :
I0
d x
0
_.m
M" (K~'K ±)
1.30 M'(K~K
GeV'
1.62 1.94 ±) G e V '
g =>
¢b)
o
3
0
.~ E -, Z
20
~
~
.
.
.
.
1(3
....
5
I0 0.98
1.30
1.62
M' (K,=K,°)
1.20
0.98
1.94
M=(K~ K ±)
GeV'
1.40
GeV'
Fig. 8. M2(KI~) spectra for five and six-body annihilations. They all show an accumulation near threshold which is interpreted by the reflection of K* and D productions (dashed curves). The full lines represent phase space. (8a) MZ(KI°K-~) in ~p --~ Kl°K=~ *Tr- (325 events) (8b) M2(K~K~) in pp --~ K~K~Tr-Tr° (327 events) (8e) M2(K~K :e) in pp ~ K~K~Tr:F (M) (259 events) (Sd) M2(K~K :e) in ~p --o K~K~-Tr:FTr+~-~° (122 events). 3. D ° QUANTUM NUMBERS 3.1. Isospin and charge conjugation of the D To d e t e r m i n e the isospin and the c h a r g e conjugation of the D, we shall use the following r e a c t i o n s : pp ~
DoJ °
,
~p ---*D~ ,
pp ~ DO .
The e x i s t e n c e of the D°¢o° final state excludes I= 2 for the D. T h e r e f o r e we shall c o n s i d e r the four p o s s i b l e a s s i g n m e n t s CD = + 1, I D = 0 or 1. An isospin d e c o m p o s i t i o n on the b a s i s of these four a s s i g n m e n t s is given in appendix A. This decomposition allows a p r e d i c t i o n to be made c o n c e r n i n g the r e l a t i v e r a t e s for D ° o b s e r v a t i o n in different final states. In p a r t i c u l a r tables 2 and 3 give t h e s e r e l a t i v e r a t e s together with the exp e r i m e n t a l o b s e r v a t i o n s for the final s t a t e s D~ and Dp r e s p e c t i v e l y . A c o m p a r i s o n of p r e d i c t i o n and o b s e r v a t i o n in the D~ final state c l e a r l y excludes the possibility ID = 1. This leaves ID = 0 as the only p o s s i b i l i t y .
[60
704
C. D'ANDLAU et al.
Table 2 Study of the isospin and the charge conjugation of the D ° with the reaction ~p ---* DTT. Hypothesis CD ID I3D
Reactions
Visibility of the K~ a)
Production ratio
Prediction
Experiment
+1
0
0
(K:eK~) o
0.590
0.196 IN o1l k 1 L2
14 • 4
-1
0
0
(K~)
0.590
0.1961N1o l kl[ 2
14:e4
+1
1
0
(K±K~?T~) 7T°
0.590
0.098 N o11~'~1 2
+1
1 :el
(K:~K~o) : F
0.590
0.147 ]k 112 N b)
(KIK 1, )
0.340
0.085 t k012 N b)
O O :e ,/i.~ (UlU2"/i")
0.590
0.147 I k I 12 Nb)
(K:eK~,% o
0.590
0.098 }~o11 kl ]2
(K:eK~ °) ~ :
0.590
0.147 ]k 1 ]2 N b)
>/ 14
(K~K~,:e) ~'~
0.340
0.042 I kl 12 N b)
>t 4.7
k o1~2 , , o y=F,) 7T:e
0.590
0.295 ] k o 12 g b)
o
O 0 4- ~:~
-1
1
0
-1
1
:el
14 c)
>~ 14
14 ± 4
o +2 -0
0+2 -0 >/ 14
14 c)
0 +3 -0
14 :e 4 0+2 -0 0 +2 -0 0 -+ 30
a) We have taken account of the probability of the K~ decays into ~+~- and of the p r o baMlity t~ see it in the b)N=~N1111~ + ~[ NollI 2. bubble chamber. c) Normalization.
L e t u s now r e p r e s e n t t h e KK~ s y s t e m a s on fig. 9. S i n c e t h e m a i n d e c a y m o d e s of t h e D l e a d to t h e K ° K + a n d KOK - s y s t e m s , w e h a v e to c o n s i d e r t h e c a s e I K ~ = 1. F u r t h e r m o r e , the n o n - v a n i s h i n g of the p o p u l a t i o n d e n s i t y of t h e D a l i t z p l o t of D ° d e c a y in the l o w m a s s r e g i o n of t h e KI~ s y s t e m (fig. 10c) i m p l i e s t h a t 1KI~ = 0 i s d o m i n a n t . T h e n G K I~ = (-1) IKF~+/K~ = - 1 , and
G D = GK~GTT = +1 . T h u s w i t h t h e a s s u m p t i o n t h a t t h e i s o s p i n of t h e D i s z e r o w e h a v e : CDO = G D O ( - 1 ) I D ° = +1 . So o u r e x p e r i m e n t a l d a t a s t r o n g l y f a v o u r t h e a s s i g n m e n t s : ID = 0
and
CDO = +1 •
T h i s c o n c l u s i o n i s c o m p a t i b l e w i t h t h e o b s e r v a t i o n s m a d e on t h e D°p ° c h a n n e l ( s e e t a b l e 3).
~p ANNIHILATION
705
Table 3 Study of the isospin and the charge conjugation of the D with the reaction ~p --* D~. Hypothesis CD ID I3D +1
-1
0
0
0
0
Reactions
Visibility of the K ~ a)
(K±K~'//"~:)~'+~-
0.590
ol 0.196 ]N 1 h I 12
10
O O O ,¢+~.(KIKI~")
0.340
0.028 IN1ol k II 2
2
6±3
o o o ?r+~(K1K27r)
0.590
0
0 -+ 30
(K±K~ ~) ~+,-
0.590
+-
+1
1
0
+1
1
±1
-1
1
0
-1
1
-1
Production ratio Prediction
0
0.196 tN1ol k 1 t2
0.340
0
o o o 7f+Tr(K1K2?I)
0.590
0.098 IN~Ilkl12
(K±K1~ ) ~'+~-
0.590
{K°lK°ffr°) ? r + -
0.340
0.098 I k N 1112 1 o 0.028 I koNilo i2
(KIKI~")
0.340
0.085 I
(K~=KI~r~:) Ir+Tr-
0.590
0.098 IkiNlo 1 12
o o o "/T+y(KIK2~")
0.590
0.098 IkoNloI 12
o o ± 7r:Fffo (K1K2Tr)
0.340
0.042 I k l t 2 N b)
Nb)
c)
10 el
Experiment 10 ± 5
10 ± 5
0
6±3
5
0 -+ 30
10 c)
10 ± 5
6 c)
6+3
>/ 12 10 c)
>13
0 +- 02 10 ± 5 0t3 -0 0 +3 -0
a) We have taken account of the probability that the K~ decays into 7r+~r- and of the probability to see it in the bubble chamber.
b) N--
. 1 1 2I 1t2÷~ %
c) Normalization.
6KK
IKK K
lKI~
K
L~
Fig. 9. A representation of the KK~ system.
3.2. Spin and parity of the D ° The spin and the p a r i t y of the D ° have b e e n a n a l y z e d by studying both its p r o d u c t i o n and its d e c a y p r o p e r t i e s . F o r this a n a l y s i s a p u r i f i e d s a m p l e of D ° e v e n t s was used: m o r e p r e c i s e l y the events c o r r e s p o n d i n g to
706
C. D'ANDLAU et al.
1.62 < M 2 (I~Tr) -.< 1.74 GeV 2 f o r r e a c t i o n s (1)-(4) with the additional r e s t r i c t i o n t h a t the D ° is p r o d u c e d in a s s o c i a t i o n with an w o f o r r e a c t i o n (1) and a pO f o r r e a c t i o n s (2) and (4). T h e e v e n t s with 1.62 --< M 2 (K~K'41r "~) < 1.74 GeV 2 of the r e a c t i o n K~K~lra:~r°, s a t i s f y the additional r e s t r i c t i o n M2(K~IC~) --< 1.1 GeV 2. T h e s a m p l e s of e v e n t s u s e d f o r e a c h r e a c t i o n a r e : ~ p - ~ D ° o __. K~lK:eTr¥Tr~-TroTr±
42 e v e n t s ,
pp ~ D ° o --. K~iC41r~Tr¥Tr±
21 e v e n t s ,
pp--* D°(M) ~ K~K±Tr~(M)
36 e v e n t s ,
~p__., D ° o ~p ~ D°Tr°
..o..o o + r~lr~l~r ~r 7r ~ K~IC47r:~lr°
7 events, 16 e v e n t s .
With t h e s e r e s t r i c t e d s a m p l e s the b a c k g r o u n d d o e s not r e p r e s e n t m o r e than 20% of the e v e n t s . 3.2.1. Study of the D ° decay. Fig. 10 s h o w s the c h a r a c t e r i s t i c d i s t r i b u t i o n s of the D ° d e c a y . F i g s . 10b and 10c s h o w no c l e a r e v i d e n c e f o r a (KTr) o r a (KI~) r e s o n a n c e . But we should still t a k e a c c o u n t of the p o s s i b l e m a n i f e s t a t i o n of f i n a l - s t a t e i n t e r a c t i o n s b e t w e e n (Krr) o r (KK~. T h e P - w a v e (Klr) i n t e r a c t i o n is well known and can be p a r a m e t r i z e d by a K*(891) B r e i t - W i g n e r f o r m u l a . C o n c e r n i n g the KI~ t h r e s h o l d i n t e r a c t i o n , we know that it is c o r r e c t l y r e p r o d u c e d e i t h e r by a B r e i t - W i g n e r o r by a s c a t t e r i n g l e n g t h p a r a m e t r i z a t i o n (ref. [6]). T h e a c c u m u l a t i o n of e v e n t s at low KI~ m a s s v a l u e s l e a d s us to b e l i e v e t h a t lKI~ = 0 is d o m i n a n t . In this c a s e the spin and the p a r i t y of the D ° a r e g i v e n by:
gDo = LTr , PDO = ( -1)LTr+l , and when we r e s t r i c t o u r s e l v e s to take only the l o w e s t value of LTr, we have to c h o o s e f o r J ~ b e t w e e n 0 - , 1 + and 2-. T h e r e f o r e , to s t u d y the d e c a y of t h e D ° we t r y t h r e e h y p o t h e s e s , f o r which we give in appendix B the m a t r i x e l e m e n t s and in t a b l e 4 the r e s u l t s of fits p e r f o r m e d . F o r t h e s e fits we have u s e d the t h r e e d i s t r i b u t i o n s g i v e n by fig. 10b, c and d, and a l s o the p r o j e c t i o n s (Tlr/Trr)max and (TK~ - TK~)/TTrmax) of the D a l i t z plot p r e s e n t e d in ref. [2]. (i) If we a s s u m e that the p o p u l a t i o n of the d e c a y D a l i t z plot (fig. 10a) is g o v e r n e d by the p r o p e r t i e s of the d e c a y m a t r i x e l e m e n t a s d e t e r m i n e d m a i n l y by its t r a n s f o r m a t i o n p r o p e r t i e s r a t h e r than final s t a t e i n t e r a c t i o n s , then the h y p o t h e s i s JDPO = 0 - can be r u l e d out and JDPO = 1 + and 2- a r e equally probable ref.[2].
~p ANNIHILATION
(a) 0.64
OJ O
707
I
(c)
¢5
t9
c
0.56
I
Hv
Q48
.".,-:./. o°
•
.
:,L I
0.40
n
•
o °
O L.
2
E=
Z I
0.48
I
I
0.56
I
1.0
0.64
O C)~
25 20
:"
15
~.~ (b) ,,,,,, """ ..... "
-,°,~
~
E
~ z 0.5 M' (KTr)
0.6 GeV'
1.3
1.4
GeV a
(d)
Z 0.4
1.2
M' (KK)
M = ( K~' "n"+) G e V '
~'c0° ~I
I.I
M= ( K K ) ~< I.I GeV =
15
-I.0
0
1.0
Cos 8 K E
Fig. 10. Decay distributions for D ° events. The full lines drawn on the spectra are obtained from the fit described in the text.
(ii) If we s u p p o s e a s t r o n g P - w a v e (K~r) i n t e r a c t i o n , J P = O- and 2- a r e r u l e d out and only J P o = 1+ is c o m p a t i b l e with the decay of the D ° (table 4) (ref. [3]). (iii) A l t e r n a t i v e l y , if we i n t e r p r e t the o b s e r v e d population density of the Dalitz plot a s e s s e n t i a l l y being due to a s t r o n g S-wave i n t e r a c t i o n between the two K m e s o n s , and the KK i n t e r a c t i o n d e s c r i b e d e i t h e r by a B r e i t W i g n e r f o r m u l a (MKI~ = 1.02 GeV, F KK = 60 MeV) or by a s c a t t e r i n g length p a r a m e t r i z a t i o n with an a b s o l u t e s c a t t e r i n g - l e n g t h value l a t running f r o m 0.7 to 2.2 f m (ref. [6]) (table 4), 0- is the m o s t f a v o u r e d a s s i g n m e n t f o r D o, 2- is v e r y unlikely and 1 + is l e s s f a v o u r e d if tal > 1.5 f m .
Prob.
oL
1.0 ± 0.08
1.0 * 0.08
1.0 ~: 0.08
80%
43.6
Prob.
80%
43.6
2 X
80%
< l0 -4
107.3 41.8
3%
73.2
60%
2.10 - 4
93.8 42.5
40%
54.8
6%
0.28 ± 0.06
0.36 ± 0.08
0.76 ~ 0.15
< 10 - 4
161.8
2 X
52.9
48.1
38.7
Prob.
35%
55%
90%
< 10 - 4
3.10 - 4
89.8
211.5
< 10 - 4
< 10 - 4
157.1
120
54.3
2-
0.37 ± 0.03
0.42 ~ 0.03
0.53 • 0.04
N o t e s : (i) The e x p e c t e d v a l u e of t h e X 2 i s 58 f o r h y p o t h e s i s (1), (2), (3), (3') and 57 f o r h y p o t h e s i s (4). (ii) (KIK)S m e a n s a (KK) i n t e r a c t i o n r e p r o d u c e d by a B r e i t - W i g n e r f o r m u l a (MKI~ = 1.02 GeV, I"K~ = 60 MeV, s e e appendix C). (iii) (KI~)s L m e a n s a (KK) i n t e r a c t i o n d e s c r i b e d by a S - w a v e s c a t t e r i n g l e n g t h p a r a m e t r i z a t i o n ( s e e a p p e n d i c C).
X
60%
45.6
2.2 f m 2
60%
44.5
1.5 f m
60%
45.6
2.2 f m
(4) +(1- q) [D ° --, K891 + K]
60%
44.5
1.5 f m
1.5 x 10 - 3
1.5 × 10 - 3
88.8
0.7 f m
88.7
D °--* (KI~)SL +
(3')
65%
41.5
< 10 - 4
0.7 f m
D °--, (KK)s + 7r
C3)
367
71.7
< 10 - 4
310.8
a [DO--, (KK)s L + y]
* +K D °--, K891
L~"
D °--, KK +~"
(2)
(1)
1+
0
Table 4 Study of the D ° d e c a y .
>
>
~p ANNIHILATION
709
(iv) Finally we can suppose that the final state (KTr) and (KK~ i n t e r a c t i o n s a r e both p r e s e n t in the D ° decay. We a r e then led to p e r f o r m a fit with the following decay m a t r i x e l e m e n t s J~Pn = 0- , lJ~
i MO12 = alM°(K*)12 + ( l - a )
JDPo= 1+ ,
I Mll 2
I M°(KI~) 12 ,
= al~. Mi(K*)Mi(K*)I +(1-a)l $
.~
Mi(K~)Mi(KI~)I ,
$
tM212 = a l ~ M/J(K*) Mij(K*)I + (1-a) I~..MiJ(K~)Mij(KI~)I , ij ~J w h e r e the explicit e x p r e s s i o n s f o r MO(K*), M / (K*), M/J(K*), M°(KK), M i ( K ~ and M/J(KI~) a r e given in appendix B; then all the t h r e e hypotheses (table 4) (JP = 0-, 1 +, 2-) give good fits, we shall only e m p h a s i z e that the lowest a s s i g n m e n t (0-) is sufficient to r e p r o d u c e the e x p e r i m e n t a l r e s u l t s . JDPo = 2- ,
3.2.2. Orientation of the decay plane. The general f o r m a l i s m needed f o r this kind of study was given by B e r m a n and J a c o b [7]. In the c a s e of our e x p e r i m e n t , it allows one to p r e d i c t the f o r m of the distribution of the angle between the n o r m a l s to the decay (nd) and the production (np) planes of the D ° [W(cos 0nd.nn)], and also of the angle between n d and the line of flight of the D ° (D) defined in the ~p c.m. s y s t e m [ W ( c o s 0 n d . D ) ] . We give in appendix C the f o r m of t h e s e distributions for J ~ o = 0-, 1 ÷, 2-. Figs. 10a and 10b give the e x p e r i m e n t a l distributions forUall D ° events. T h e s e distributions a p p e a r to be i s o t r o p i c and do not allow us to distinguish between the different s p i n - p a r i t y h y p o t h e s e s for the D ° . But again one should note that the hypothesis JP = O- is sufficient to r e p r o d u c e them. ~ p .--I~ D° X °
40
(o)
(b)
O" E z
0 0
÷1 cos OND D
0
+1
cos ~ND.NP
Fig. 11. (a) Distribution of coSOBp .nd =rip .nd/(Inp[ [ndl) wherenp is the normal vector to the ~p production plane and Bd the normal vector to the decay plane of the D° . (b) Distribution of cos end./} =Bp .D/(IBpl ID~ w h e r e / ) is the vector characterizing of the line of flight of the DO.
710
C. D'ANDLAU et al.
4. CONCLUSION
In our study we have established a l m o s t without ambiguity the isospin (ID = 0) of the D °, and have shown that, for the c h a r g e conjugation, C D = +1 is favoured. For the spin and p a r i t y , the study of the decay and the production of the D ° does not f a v o u r any one of the t h r e e lowest spinp a r i t y a s s i g n m e n t s (0-, 1 +, 2-) compatible with the assumption lK~ = 0 suggested by the accumulation of the (KI~) m a s s e s at low values. However J P o = 0- is enough to r e p r o d u c e all the decay and production distributions, p~'ovided we take into account a s t r o n g (KK)I= 1 i n t e r a c t i o n at threshold, as seen in p a r t i c u l a r in ~p annihilations at r e s t in the t h r e e body channel KK~r.
APPENDIX A If we denote by k 0 and k 1 the amplitudes c o r r e s p o n d i n g to I(KK--) = 0 and I(KK~ = 1 r e s p e c t i v e l y , the decay amplitudes f o r the D into different obs e r v a b l e charge modes are: CD = +1, ID = 0: D ° =__kl [ ( K + K ~ -) - (K+K~Tr-) + ( K - K ~ "+) + ( K - K ~ "+) - (K+K-lr °)
4g
o
o o
1 {(K~K~ o) + ( K 2 K 2 ~ ) } ] .
CD = +1, ID = 1: D°
o o o ko [(K+K-Tro) _ 1 {(K~K~ITo) + (K2K2~)}]
+
-
1 o o:~ o o* D + = ~k o [(K+K-Tr +) --~{(K1K17T ) + (K2K2~)}]
+ ½k1 [(K=eK~Tro) $ (K~g~Iro) _ (K+K- r±) _ (K1K2~ r o o ~-)] . CD = -1, ID = 0: D ° =---~
_
(K+K- o)
o o o _ (K1K2~r)]
CD = -1, ID = 1: D ° = __k° [(K+K- o) _ (K1K2~O o o)] + ~k l l [(K+K~Tr-) _ ( K + K ~ -) - (K-K~
+) - ( K - K ~ . + ) ]
,
711
~p ANNIHILATION
- ½k1 [(K-~K~Tr°) ¥ (K'~K~Tr°) - (K+K-Tr+) 1
o o ±
V~ {(KIKI~ ) +
(K~I~+)}]
W e have seen that D is produced in association with a system X (co°, p, y, z;°), so we shall study final states of the form ~p ~ D ° X o . For ID = 0:
[DX>= N°°I D°X°> + N°II D°X° >. For ID = 1:
11
IDX> = ~i 0 ]D°X°>
No
+ (_N~o31 N11
iDoxO> Nlo1
) Io-x+>,
wnere' -Iv"Ipp ID' I x is the t r a n s i t i o n amplitude and ID, IX, Igp the isospin of the X s y s t e m and of the ~p s y s t e m . Of course the unique N/D' IX symbol l~p we use, depends on the charge conjugation and spin-parity assignment of the D together with the quantum n u m b e r s of the initial states.
APPENDIX B K K interaction:
-Mo(KK-) = 9
or BW(KI~) with ~9 = l + i a p1 ~ '
I~1 = 0"71 1.5 fm 2.2
or Bw( ) M _Ms2÷eMsrs M S = 1.02 GeV (ref. [5]) ,
_Mi(I¢~) = pi BW ( K ~ ,
F S = 60 M e V .
712
C. D'ANDLAU et al.
I
*"
p~ is the momentum of the ~ in the c.m. system of the D °. (K~')/=I interaction: Mo(K* ) = PK17r "PK2 BW (K~) +PK2~ "PK 1BW (K~.) , MiJ (K*)
=
i j [PK17r PK i
j
" Pk" 2 ~ 5 ij (PK17r .PK2) ] BW(K~) 2 +P3K17r -
j
i
2
""
*
+ [PK2~PK1 +PK27rPK 1 - ~ 5Z3(PK2~r"PK1)] BW(K 2) , i
,
M i (K*) = [ b Ei 1~ BW (K;) + PK27r BW (K2) ] ,
withPKm = momentum of K m in the c.m. system of the D, P K n ~ = momentum of Kn in the c.m. system of KnY, BW (I~) = M~m~
1 M 2 , + i M K , FK,
APPENDIX C
JDo o-
W (cOs0nd n p ) = ct , W(cos Ond.D)
= ct .
W (cos Ond.np ) = A 0 + A 1 cos 0 +A 2 cos 2 O ,
JDo= 1+t W(cos0nd.D )
= B O+B 2cos 20 .
i W(cos Ond.nP)=n~=O A o c o s n 0 , JDPo = 1- ~W(cos Ond.D ) = B0+B 2 cos20 + B 4 cos49 . We would like to thank Dr. S. Wojcicki for many stimulating discussions, and Professor Ch. Peyrou and Dr. R. Armenteros for their continuous support.
~p ANNIHILATION
713
REFERENCES [1] J. Barlow, E. Lillestdl; L. Montanet, L. Tallone-Lombardi, C. d'Andlau, A. Astier, L. Dobrzynski, S. Wojcieki, A.M. Adamson, J. Duboc, F. James, M. Goldberg, R.A. Donald, R.~lames, J. E. A. Lys and T. Nisar, Nuovo Cimento 5OA (1967) 701. [2] Ch. DTAndlau, A. Astier, M. Della-Negra, L. Dobrzynski, S. Wojcicki, J. Barlow, T. Jacobsen, L. Montanet, L. Tallone, M. Tomas, A.M. Adamson, M. Baubillier, J. Duboc, M. Goldberg, E. Levy, D.N. Edwards and J. E. A. Lys, Phys. Letters 17 (1965) 367. [3] D.H. Miller, Suh Urk Chung, Orin I. Dahl, R.I. Hess, L.M. Hardy, J. Kirz and W. Koellner, Phys. Rev. Letters 14 (1965) 1074. [4] J. Duboc, A. Minten and S. Wojcicki, CERN Report 65-2. [5] A. Rosenfeld, A. B a r b a r o - G a l t i e r i , W. Podolsky, L.R. P r i c e , P. Soding, Ch. Wohl, M. Roos and W. Willis, Revs. Mod. Phys. 39 (1967) 1. [6] A. Astier, J. Cohen-Ganouna, M. Della-Negra, B. Marechal, L. Montanet, M. Tomas, M. Baubillier and J. Duboc, Phys. Letters 25B (1967) 294. [7] S. M. Berman and M. Jacob, Phys. Rev. 139B (1965) 1023.
Nuclear P h y s i c s B5 (1968} 693-713. North-Holland Publ. Comp., A m s t e r d a m
ANTIPROTON-PROTON (K~
+ 3y)
AND
STUDY
OF
ANNIHILATION (KK THE
+ 47r) A T D°
1.2
INTO GeV/c
PROPERTIES
C. D'ANDLAU~ A. ASTIER~ L. DOBRZYNSKI, J. SIAUD Laboratoire de Physique Nucl~aire, Collbge de France. Paris J. BARLOW, L. MONTANET, L. T A L L O N E - L A M B A R D I * CERN, Geneva, Switzerland
A. M. ADAMSON, J. DUBOC, M. G O L D B E R G Institut de Physique Nucl$aire, Paris
R. A. DONALD, D . N . EDWARDS, J . E . A . LYS ** Nuclear Physics Research Laboratories, Liverpool
Received 12 March 1968
A b s t r a c t : Experimental r e s u l t s a r e p r e s e n t e d for the five- and six-body annihilations ~p --~ KK'3~ and ~p --~ KK 4~ of 1.2 GeV/c antiprotons. Analysis of these r e sults in t e r m s of production of K*(890), p , co. ~ and D(1280) resonances is made. A detailed analysis of the quantum numbers for the D - m e s o n is given.
1. I N T R O D U C T I O N In t h i s p a p e r , w e p r e s e n t a s y s t e m a t i c a n a l y s i s of t h e f o l l o w i n g s i x - a n d f i v e - b o d y ~p a n n i h i l a t i o n s a t 1.2 G e V / c : ~p -~ K~K-'e~:~+~-~ °
(122 e v e n t s )
,
(1)
~p -~ K ~ K = e ~ + ~ -
(325 e v e n t s )
,
(2)
~p - - K ~ K - ~ ( M )
(259 e v e n t s )
,
(3)
(327 e v e n t s )
,
(4)
(539 e v e n t s )
,
(5)
.o.o
+
-
~p ~ ~ 1 ~ 1 ~ ~ ~ pp ~ K~ (M) ~+~-
o
* Now at Instituto di F i s i c a . Milan. ** Now at University of Michigan. Ann Arbor, USA.
694
C. DIANDLAU
et al.
where (M) stands for m i s s i n g p a r t i c l e s in r e a c t i o n s (3) and (5). Reaction (1) is the only abundant six-body channel o b s e r v e d for this e x p e r i m e n t : O O+ other s i x - b o d y channels, such as ~p -~ KIK17r 7r (M), and ~p --~ K~(K°)zr¢~-~r+~r- have much s m a l l e r c r o s s s e c t i o n s (see table 1). As is shown l a t e r , the observation of r e a c t i o n (1) is mainly due to the p r o d u c tion of co° -~ ~r+~r-Tr° which cannot contribute to s i x - b o d y annihilations with four c h a r g e d pions. We can t h e r e f o r e safely a s s u m e that m o s t of the events (3) a r e five-body annihilations, with 2~ ° m i s s i n g , except for a few events with an 77° or an w ° decaying via t h e i r neutral modes. In r e a c t i o n (5), we have at l e a s t one K ° and ~o m i s s i n g , but we cannot exclude that a good f r a c t i o n of these events a r e six-body annihilations with one K ° and 2~ o missing, this last final state being f a v o u r e d by the p r o d u c t i o n of w °, a s in r e a c t i o n (1). A s i m i l a r a n a l y s i s of the two-, t h r e e and f o u r - b o d y annihilations at 1.2 G e V / c is a l r e a d y published (ref. [1]). One of the most i n t e r e s t i n g r e s u l t s of this a n a l y s i s is the o b s e r v a t i o n of a new S= 0 r e s o n a n c e , the D °, a l r e a d y r e p o r t e d in refs. [2,3]. This p a p e r s u p e r s e d e s r e s u l t s p r e s e n t e d in ref. [2]: in p a r t i c u l a r , we p r e s e n t h e r e a m o r e detailed a n a l y s i s of the D - m e s o n b a s e d on its o b s e r v a t i o n in the "two-body" annihilation p r o c e s s e s : pp .... D°X ° , where X ° can be identified to co°, 7 °, pO or ~o. The r e s u l t s were obtained f r o m an a n a l y s i s of ~p annihilations involving at l e a s t one visible K~ decay. The film under study was taken in the Saclay 81 cm HBC exposed to a b e a m of 1.18 ± 0.01 G e V / c ~ f r o m the C E R N , .{ (ref. [4]). The r e s u l t s p r e s e n t e d c o r r e s p o n d to the complete film sample, that is roughly 5 events/rib. E a c h event was weighted in o r d e r to c o r r e c t for the finite probability of the K~ to d e c a y outside the visible r e g i o n of the c h a m b e r and for the p r o bability that the K~ d e c a y s within 0.2 c m f r o m the production apex. T h e s e weights were used when n e c e s s a r y in the following a n a l y s i s , p a r t i c u l a r l y f o r the calculation of the c r o s s sections, for which we have also taken o into account the neutral decay mode of the K 1 and the scanning efficiency.
2. RESONANCE
PRODUCTION
IN (KI~ + 3~) AND
(KI~ + 4~) FINAL
STATES
T h e s e five- and six-body annihilations a r e dominated by the production of K*(891), p(765) and 0)o(780). The K*(891) and c0(780) production shows up c l e a r l y on fig. 1 and 3, whilst the p(765) p r o d u c t i o n just i n t r o d u c e s a r e l a t i v e l y s m a l l distortion of the (~g) s p e c t r u m (fig. 2). In addition, the neutral (KI~) m a s s s p e c t r u m has a g e n e r a l tendency to show an enhancement for all these r e a c t i o n s around 1290 MeV. This enh a n c e m e n t shows up much m o r e c l e a r l y when the p a r t i c l e s which a r e left outside the neutral (KI(~) combination f r o m a r e s o n a n t state, such as ¢0°, p o ~?o (fig. 4, 5). It has been shown in ref. [2] that the (KI~Tr) enhancement cannot be attributed to the reflection of the r e s o n a n c e s a s s o c i a t e d to its
~p ANNIHILATION
12C
t ~
695
(o)
(c) 0
~,
o
8O
0
(.9 >,
0
d
6O
40
E
0.40 ID
0.72
1.04
ld = ( K "tr)
O
2O
:3 Z
0
0.40
1.36
1"== I / 2
0.72
1,04
MZ(K..n -)
GeV =
1.36
GeV =
3, (M O
c~
(b)
.
50 i
¢n
,ID
E
C ¢D
z
25 $
4C
.D
E_ Z
0.40
0.72
1.04
M = (K'rr)
1.36
GeV =
i
0.40
i
I
i
0.60
0.80
M = (K'n')
T==I/2
"--'I'~"I~
r~
1.00 GeV z
Fig. 1. M2(KTr) distributions for five- and six-body final states. Full lines represent phase-space curves. T (la) M2(K~) in pp ~ K~K±~T~±~ . The dashed line corresponds to production of 65% K*, 26~p and 9% D°. (325 events - 4 combinations per event). (lb) MZ(Ky) in pp --~ Kl°K~?r+~-Tr°. The dashed line takes account of a production of 40% K*, 14%p, 44% Wo and 2% D°. (327 events - 6 combinations per event). (lc) M2(K~) in pp --~ K°K~-?rT(M). The dashed line was obtained for a production of 69% K*, 13%p and 1 8 ~ D °. (259 events - 2 combinations per event). (ld) M2(K~") in ~p --~ K~>K!yT~'~'~:Y °. The dashed line corresponds to a production of 46% D°W o, 19% KK~c0- and 35% K*KyyTr. (122 events - 6 combinations per event).
p r o d u c t i o n , a n d m u s t b e i n t e r p r e t e d a s a g e n u i n e r e s o n a n c e , the D - m e s o n , with M= 1290±TMeV,
F= 30+ 5MeV.
T a b l e 1 g i v e s t h e r e s u l t s of t h e f i t s p e r f o r m e d on a11 t w o - a n d t h r e e b o d y m a s s s p e c t r a . I n t h e f i t t i n g p r o c e d u r e , we have g e n e r a t e d , by M o n t e C a r l o t e c h n i q u e s , s t a t i s t i c a l d i s t r i b u t i o n s c o r r e s p o n d i n g to the p r o d u c t i o n s of K*, p, w° , D ° a n d ( D ° X ° ) , w h e r e X ° i s f o r w °, pO, 77o. We h a v e n o t t r i e d s i m u l t a n e o u s r e s o n a n c e p r o d u c t i o n s , l i k e (K*Kp), (K*K*Tr) . . . . . ,
696
C. D ' A N D L A U et al.
Q o
I00
150
_,so=.g
901~~,_ ]
_.
,;
\i '
40
so
zo
30
E 004
O.ZO 034. 0.50 0,66
M=('rr'rr)
Tz : 0
0.04 0 2
GeV =
M=('rr'rr)
0.4
0.6
Tz : 0 , 1
0178
GeV =
Fig. 2. M2(~TT) d i s t r i b u t i o n s f o r f i v e - b o d y f i n a l s t a t e s . Full l i n e s a r e p h a s e - s p a c e curves. • -0 ± = F - F (2a) M2(?T~) m pp---* KIK ?T ~ ~ . The dashed line takes account of a production of 65%K*, 26% D, and 9~oD°. ~325 ecents - 2 combinations per event). (2b) M2(77~') in ~p --* K~.K~y ~-~.o. The dashed line takes account of a production of 40%K*, 14%p, 44%¢0 and 2% D°. (327 events - 3 combinations per event).
-> (o)
(b)
(.9 OJ
o o
50
o~ =-. 40 G J,
30
E
20
20
I0
I0
Z
020
0.36
0.52
0.68
M = (-n "+ " r r - "n" ° )
0.84 GeV =
1.00
02
0.4 M=
06
0.8
GeV =
0 0 +Fig. 3. ( a ) M 2 ( ~ + ~ - ~ o) in ~p ~ KIK17T ~" 7r0 . The full line r e p r e s e n t s the p h a s e s p a c e d i s t r i b u t i o n - t h e d a s h e d l i n e t a k e s a c c o u n t of a p r o d u c t i o n of 40% K*, 14% p, 44% co ° and 2% D ° . (327 e v e n t s ) . (b) M i s s i n g m a s s s q u a r e d s p e c t r u m in ~p ~ K~K-~=F(M). (259 e v e n t s ) . The h a s h e d h i s t o g r a m r e p r e s e n t s t h e s p e c t r u m o b t a i n e d f o r the e v e n t s s a t i s f y i n g the c u t s : 1.64 GeV 2
~p ANNIHILATION
697
(a) 30
20
~> (..9 O
O M ' (K,° K± ~r ~) O'3
0,J
2C
GeVt
(b)
D°
IE 12
8
o 4
M ' ( K ~ ° K,° "rr = )
E
GeV'
(c)
=1
z
D°
[
ac
15
" ;
I0
140
1.80
2.20
M ' ( K~° K:t: Tr :1: )
260
300
GeV'
Fig. 4. M2(KKTr ) d i s t r i b u t i o n s f o r the five body s t a t e s . Full l i n e s r e p r e s e n t p h a s e space curves. (4a) M2(K~K~-Tr +) in pp--+ Kl°K±lr~:y+?r- . The d a s h e d l i n e t a k e s a c c o u n t of a p r o d u c t i o n of 65% K*, 25% p a n d 9% D o. (325 e v e n t s - 2 c o m b i n a t i o n s p e r event). The h a t c h e d h i s t o g r a m r e p r e s e n t s the s p e c t r u m o b t a i n e d f o r the e v e n t s s a t i s f y i n g the cut M2(KK) < 1.08 GeV 2 , w h i c h is m a d e to a c c e n t u a t e the p r e s e n c e of the D o . o o" ) m • -pp --~Kl°Kllr o + - oY ~ • T h e d a s h e d h •n e t a k e s a c c o u n t of a p r o d u c t i•o n (4b) M 2 (KI°KI~ of 40% K * , 14% p, 44% 0ao and- 2% D u. (327 e v e n t s - 1 c o m b i n a t i o n p e r event). The h a t c h e d h i s t o g r a m is defined a s in 4a. (4c) M2(KI°K4-~ :F) in ~p--+ Kl°I~±~r~(M). The d a s h e d l i n e t a k e s a c c o u n t of a p r o d u c t i o n of 69% K*, 13% p and 18% D °. (259 e v e n t s - 1 c o m b i n a t i o n p e r event). The h a t c h e d h i s t o g r a m is d e f i n e d a s in 4a.
698
C. D'ANDLAU et al.
Do
125 I0
7.E 5
eNI > (D 0
~ 4
ci
2
(_9
(o)
25
,L
)
6
GeV' (b)
L
o
ww(2 > Q~
M ' ( K , ° K~'n"°)
4
--,L----
,_,.._k__
GeV'
~
(C)
I
.____~__.__,___
(KT K"Tr °)
o
GeV'
16
E 2:}
Z
12 8 4
0
(KK~')°GeV'
4 2
oi__ 1.48
1.60
IBO
2 O0
M 2 ( K , K, Tr±)
220
2.40
GeV 2
Fig. 5. D p production MZ(KK~r) s p e c t r u m in f i v e - b o d y annihilations ~p ---* (KK?r)(~rTr ) when cuts a r e applied on the r e c o i l e d dipion (Trlr) to a c c e n t u a t e the p production. F o r the n u m b e r of DO expected, see table 3. (5a) M2(K~K±TrT) in ~p ~ K~K±?r=F?r+Tr- with 0.49 < M2(?r+y-) < 0.64 GeV 2. The full line r e p r e s e n t s (KK~p) phase space. The dashed line takes into account the D ° p ° production. (hb) M2(K~K°?r °) in ~p ---* K~K°Tr°Tr+y - with 0.49 < M2(y+~r-) < 0.64 GeV 2. (5c) M 2 ( K ~ K ~ °) i n , p - - . KOi~O 1( ~ 0 )?r + 7r with 0.49 < M2(?T+~r-) .< 0.64 GeV 2. (5d) Sum of h i s t o g r a m s 5a, 5b. 5c. o o q- in ~p ---, K1KI~ o 0 + 7r-lro with 0.49 < M2(Tr-+Tr°) < 0.64 GeV 2. One does (5e) M 2 (K1K~lr) not see any D ± production, as e x p e c t e d if I(D) - 0.
~p ANNIHILATION
699
M z ( -rr+ -n-- .rr ° )
(b)
o, cjl
25 %
2,3
_O ~ O REGION : o j o',
4•
2.1
"ee
->
i
.....:...-,!
(..9 A
.i' i)"::i
1.9
°x-
1.7
-=
. . . . . .
r
.......
r . . . . . . . . .
:,-
v
~ - . - - - -,;V
-ti
. . . . . . . . . . . . .
1.5
1.3
' b '!
:; "J (O)
I.I 0
:l__ i
L
i
~
0.2
_
i
,i
0.4
2
o
•
•
2
+
-
o
~
0.8
0.6
MZ(-n-+vr--rr °) •
io~ ,
o
GeV z •
•
•
o
Fxg. 6. M (KIK_ 7r ) = f [ M (ff lr lr )] i n ~ p - - * K i K _ 7~ 7r 7T~ . Two_ points+_ p e r e v e n t . D i s t r i b u t i o n s (a) c o r r e s p o n d to the p r o j e c t i o n of p o i n t s ( p a i r (KKTr, ~ lr ~ o) with o w h e r e a s d i s t r i b u t i Q n s (b) (dashed) c o r r e s p o n d to the M 2 (y ÷lr-lr o ) n e a r e r to M 2 (CO),
projection of crosses (pair (KK~, ~+y-~o) with Mz(~+~-IT°) farther from M~(W°)).
except for (D°X°). In the fitting procedure, we take account of only the decay p r o p e r t i e s of the resonances. For the D-meson, we use the following s q u a r e d m a t r i x element: iM(D)12 = tp . B w ( D ) 12, where 1
BW(D) M~,-M~o + iMDOrDo
700
C. D'ANDLAU
MDo = 1290 MeV ,
p=
et al.
FDO = 30 MeV ,
1 1 +iaPK~ '
a is the s c a t t e r i n g length for the KK t h r e s h o l d I= 1 interaction (lal = 2.0 f), and ~ is the m o m e n t u m of the K in the KI{ c.m. s y s t e m . We introduce P to take account of the disintegration p r o p e r t i e s of the D ° . This f a c t o r r e p r o d u c e s the a c c u m u l a t i o n of events at the t h r e s h o l d of M2 (KK). The f o r m adopted h e r e f o r P supposes that the s p i n - p a r i t y of the D ° is 0-. Note that another a s s i g n m e n t (1 +, 2-) for the D ° would not change the r e s u l t s of our study. (See sect. 3). F o r the m a s s e s and widths of K*, p and w, we use the values of ref. [5]. F o r the r e a s o n s given in the introduction, we do not t r y a fit f o r r e a c O + tion (5): ~p -~ KI~ 7T (M), but limit o u r s e l v e s to qualitative s t a t e m e n t s . We have also included in table 1 the r e s u l t s obtained for the f o u r - b o d y annihilations ~p -~ K~K~Ir-~ °, since it a p p e a r s to be an i n t e r e s t i n g channel for the D ° production. A m o r e detailed a n a l y s i s of this r e a c t i o n is given in ref• [1]. The r e s u l t s p r e s e n t e d in table 1 call f o r the following r e m a r k s : (i) Reaction (I): ~p -* K ~ K ~ y ~ + ~ - ~ ° is dominated by w ° production• M o r e o v e r , a l a r g e f r a c t i o n of this w ° production is a s s o c i a t e d with D ° p r o duction, so that 46% of r e a c t i o n (I) r e d u c e s to the p r o c e s s pp - . D ° ¢0°, with D ° ~ K~I~?r¥ and co° -~ ~+~-yo. The s c a t t e r d i a g r a m (fig. 6) i l l u s t r a t e s this situation. (ii) Reaction (2): ~p ~ K~K:ey~-y+ - is dominated by K*(891) p r o d u c t i o n and, to a s m a l l e r extent, by p(765) production. As with the coo in r e a c t i o n (i) a selection on pO p r o d u c t i o n in r e a c t i o n (2) enhances the o b s e r v a t i o n of the D ° , thus giving evidence f o r the p r o c e s s : ffp ~ D°p ° , with D ° --* K~K±~ "7-and pO ._, 7T+TT- .
(iii) Reaction (3) c o n s i s t s mainly of f i v e - b o d y annihilations pp --* K ~ K ~ ° v ° with 2~ ° missing. Its a n a l y s i s is t h e r e f o r e difficult. Howe v e r , it p r o v i d e s an i n t e r e s t i n g r e s u l t on the D ° production; namely, when a selection on D ° is p e r f o r m e d , the m i s s i n g m a s s s p e c t r u m shows a tendency to a c c u m u l a t e around the ~1o m e s o n and, to a s m a l l e r extent, around the w ° (fig. 3b) leading to the p r o c e s s e s : pp ~ D%?°
with
D ° __. K ~ K ~
~p --* D°¢~°
with
D °--* K ~ I ~ ~
,
~ o _.. all n e u t r a l s , w °-~ all n e u t r a l s
The evidence of pp --* D°w ° is m a r g i n a l , but not inconsistent with the observation of ~ 56 events for the channel ~p --* D°w ° with ~o __. ~+~r-~o [ r e a c tion (1)].
~p A N N I H I L A T I O N
701
Table 1 Cross sections. Reactions . 0.±
:F ~
pp--*~ll~
Observed 0
::F
0
g ~ y ?r
KIK
f i n a l s t a t e a)
4- :F . 0
, w
21.0 ± 3.0
D ° + 7/°
0.5 ± 0.5
K* + Ky~y ~p "-* K~K±Tr%~?r ±
325 events .0.4-
~p--~lXl~
~
:F
(M)
~0.0
Op ~ h l l ~ l ~
+-
0
7r ?r
o.
±
~:
D ° + ~Y
3.2 ± 2.0
D ° +po
3.2±
51.5+ 5.0
D ° + (M)
9.2 ± 3.5 2 . 6 ± 1.1
D ° + 00°
1.7± 0.8
p + KKTr a)
9.6 ± 5.0
-±0
75 ± 9
74.0 ± 10.0 82.0 ± 5 . 0 p
:FO
2 6 . 0 + 9.0
D°P °
4 . 0 ± 2.0
K* + y (M)
abundant
DO/)O
compatible with zero
DO o
o
105 ± 10
1.5
D ° + 770
(l~ll~l~)
539 e v e n t s .
70.5 ± 4 . 0 2 8 . 4 ± 5.0
...0..0
pp ~ K ~ + ~ (M)
p p --,lXliX ~ ~
K* + K~y po + KKy
K * + KTT~ KO-O o 1KI¢O
327 e v e n t s
46 ± 6
16.0 ± 6.0
K* +K(M)
259 e v e n t s
ff t o t a l (~tb)
8.7-3.0
D ° + 0)° 122 e v e n t s
ff p a r t i a l (~tb)
186 ± 17
198 ± 15
11.2 ± 3 . 0
1632 e v e n t s
594 ± 24
~p-"~ K1K~T+~-(?T O~'O)
5 ± 2
5 events 0
0
4- -
+
-
~ p - ~ K I ( K )~ ~ ~ ~
7±3
14 e v e n t s a) T h i s f i n a l s t a t e i s e s t i m a t e d ..o.
by its reflections o
+
-
e f f e c t s on t h e o t h e r d i s t r i b u t i o n s .
o
(iv) Reaction (4) ~p-~ ~1~1 ~ ~ ~T is dominated by w° and K*(891) production. However, there is a slight indication of D ° production associated to p ° production, while no such effect is observed for the charged (KI~) combinations when a selection is performed on the charged p (fig. 5b, 5e). (v) There is no sign of D ° production in reaction (5): ~ p - Ky~+~-(M), even when a selection is performed on the pO (fig. 5c). (vi) T h e p e r c e n t a g e of s t a t i s t i c a l b a c k g r o u n d f o r e a c h of t h e s e r e a c t i o n s was found to be consistent with zero.
702
C. D'ANDLAU et al.
In a d d i t i o n to t h e s e r e m a r k s , one s h o u l d n o t i c e t h e a b s e n c e of l a r g e E ° p r o d u c t i o n in t h e s e r e a c t i o n s , in c o n t r a s t w i t h t h e s i t u a t i o n o b s e r v e d w i t h ~p a n n i h i l a t i o n s a t r e s t w h e r e t h e E ° m e s o n d o m i n a t e s m o s t of t h e f i v e body reactions. The important accumulation observed for the neutral ( K I ~ ) s p e c t r u m b e t w e e n 1350 a n d 1550 M e V c a n b e a c c o u n t e d f o r by t h e r e f l e c t i o n of K* p r o d u c t i o n , w i t h o u t a n y n e e d of E ° a n d f* p r o d u c t i o n (fig. 4). A s e l e c t i o n on l o w (KK~ m a s s e s , w h i c h i s k n o w n to e n h a n c e t h e o b s e r v a t i o n of t h e E ° in ~p a n n i h i l a t i o n s a t r e s t , d o e s not l e a d to a b e t t e r e v i d e n c e f o r E ° p r o d u c t i o n in ~p a n n i h i l a t i o n s a t 1.2 G e V / c (fig. 7). C o n c e r n i n g t h e f*, t h i s n e g a t i v e r e s u l t i s in a g r e e m e n t w i t h t h e a b s e n c e of f* in - w h e r e the w e l l known d e c a y m o d e f * - c o u l d be o b s e r v e d ( r e f . [1]). T h e (KK) s p e c t r a o b s e r v e d f o r r e a c t i o n s (1) to (4) g e n e r a l l y p e a k a t t h r e s h o l d (fig. 8) a s w i t h t h e f o u r - b o d y r e a c t i o n s ( r e f . [1] a n d f o r p p a n n i h i l a t i o n s at r e s t ( r e f . [5]). H o w e v e r in c o n t r a s t w i t h t h e i n t e r p r e t a t i o n g i v e n f o r pp a n n i h i l a t i o n s a t r e s t , one c a n n o t e x c l u d e t h a t in t h e p r e s e n t c a s e , t h i s d i s t o r t i o n of t h e (KI~ s p e c t r a i s e x c l u s i v e l y d u e to t h e p r e s e n c e of t h e D ° m e s o n , a t l e a s t f o r c e r t a i n s e t s of q u a n t u m n u m b e r s JP (D), a s we s h a l l s e e in s e c t . 3 of t h i s a r t i c l e .
-> ~'- 6 o
_.= g4
o
2
z
0 2.0
2.2
M1 (K:' K==~r ' )
2.4
GeV =
2 O + :~ . O • :F + F i g . 7. M (K1K Tr ) m ~ p - ~ K1K ~ ~ ~ when cuts a r e applied to theM2(KTl)and M2(KK) to accentuate a possible production of E ° meson. The cuts applied are:
~ p - o K.K2~-2~3 ,
K*---*KI~ 1
M2(KI~I) n e a r e r to M2(K *) = 0.79 GeV 2 0.7 GeV 2 < M2(Klnl) < 0.90 GeV 2 M2(KK.) < 1.1 GeV 2 . The curve takes account of K*, p and D production, as well as of the outs p e r f o r m e d on the reaction. There is no sign of E ° production (M2(E) = 2.04 GeV2).
~p ANNIHILATION
703
(a)
(c)
N
>,~
3
0
30
~
20
2O :
I0
d x
0
_.m
M" (K~'K ±)
1.30 M'(K~K
GeV'
1.62 1.94 ±) G e V '
g =>
¢b)
o
3
0
.~ E -, Z
20
~
~
.
.
.
.
1(3
....
5
I0 0.98
1.30
1.62
M' (K,=K,°)
1.20
0.98
1.94
M=(K~ K ±)
GeV'
1.40
GeV'
Fig. 8. M2(KI~) spectra for five and six-body annihilations. They all show an accumulation near threshold which is interpreted by the reflection of K* and D productions (dashed curves). The full lines represent phase space. (8a) MZ(KI°K-~) in ~p --~ Kl°K=~ *Tr- (325 events) (8b) M2(K~K~) in pp --~ K~K~Tr-Tr° (327 events) (8e) M2(K~K :e) in pp ~ K~K~Tr:F (M) (259 events) (Sd) M2(K~K :e) in ~p --o K~K~-Tr:FTr+~-~° (122 events). 3. D ° QUANTUM NUMBERS 3.1. Isospin and charge conjugation of the D To d e t e r m i n e the isospin and the c h a r g e conjugation of the D, we shall use the following r e a c t i o n s : pp ~
DoJ °
,
~p ---*D~ ,
pp ~ DO .
The e x i s t e n c e of the D°¢o° final state excludes I= 2 for the D. T h e r e f o r e we shall c o n s i d e r the four p o s s i b l e a s s i g n m e n t s CD = + 1, I D = 0 or 1. An isospin d e c o m p o s i t i o n on the b a s i s of these four a s s i g n m e n t s is given in appendix A. This decomposition allows a p r e d i c t i o n to be made c o n c e r n i n g the r e l a t i v e r a t e s for D ° o b s e r v a t i o n in different final states. In p a r t i c u l a r tables 2 and 3 give t h e s e r e l a t i v e r a t e s together with the exp e r i m e n t a l o b s e r v a t i o n s for the final s t a t e s D~ and Dp r e s p e c t i v e l y . A c o m p a r i s o n of p r e d i c t i o n and o b s e r v a t i o n in the D~ final state c l e a r l y excludes the possibility ID = 1. This leaves ID = 0 as the only p o s s i b i l i t y .
[60
704
C. D'ANDLAU et al.
Table 2 Study of the isospin and the charge conjugation of the D ° with the reaction ~p ---* DTT. Hypothesis CD ID I3D
Reactions
Visibility of the K~ a)
Production ratio
Prediction
Experiment
+1
0
0
(K:eK~) o
0.590
0.196 IN o1l k 1 L2
14 • 4
-1
0
0
(K~)
0.590
0.1961N1o l kl[ 2
14:e4
+1
1
0
(K±K~?T~) 7T°
0.590
0.098 N o11~'~1 2
+1
1 :el
(K:~K~o) : F
0.590
0.147 ]k 112 N b)
(KIK 1, )
0.340
0.085 t k012 N b)
O O :e ,/i.~ (UlU2"/i")
0.590
0.147 I k I 12 Nb)
(K:eK~,% o
0.590
0.098 }~o11 kl ]2
(K:eK~ °) ~ :
0.590
0.147 ]k 1 ]2 N b)
>/ 14
(K~K~,:e) ~'~
0.340
0.042 I kl 12 N b)
>t 4.7
k o1~2 , , o y=F,) 7T:e
0.590
0.295 ] k o 12 g b)
o
O 0 4- ~:~
-1
1
0
-1
1
:el
14 c)
>~ 14
14 ± 4
o +2 -0
0+2 -0 >/ 14
14 c)
0 +3 -0
14 :e 4 0+2 -0 0 +2 -0 0 -+ 30
a) We have taken account of the probability of the K~ decays into ~+~- and of the p r o baMlity t~ see it in the b)N=~N1111~ + ~[ NollI 2. bubble chamber. c) Normalization.
L e t u s now r e p r e s e n t t h e KK~ s y s t e m a s on fig. 9. S i n c e t h e m a i n d e c a y m o d e s of t h e D l e a d to t h e K ° K + a n d KOK - s y s t e m s , w e h a v e to c o n s i d e r t h e c a s e I K ~ = 1. F u r t h e r m o r e , the n o n - v a n i s h i n g of the p o p u l a t i o n d e n s i t y of t h e D a l i t z p l o t of D ° d e c a y in the l o w m a s s r e g i o n of t h e KI~ s y s t e m (fig. 10c) i m p l i e s t h a t 1KI~ = 0 i s d o m i n a n t . T h e n G K I~ = (-1) IKF~+/K~ = - 1 , and
G D = GK~GTT = +1 . T h u s w i t h t h e a s s u m p t i o n t h a t t h e i s o s p i n of t h e D i s z e r o w e h a v e : CDO = G D O ( - 1 ) I D ° = +1 . So o u r e x p e r i m e n t a l d a t a s t r o n g l y f a v o u r t h e a s s i g n m e n t s : ID = 0
and
CDO = +1 •
T h i s c o n c l u s i o n i s c o m p a t i b l e w i t h t h e o b s e r v a t i o n s m a d e on t h e D°p ° c h a n n e l ( s e e t a b l e 3).
~p ANNIHILATION
705
Table 3 Study of the isospin and the charge conjugation of the D with the reaction ~p --* D~. Hypothesis CD ID I3D +1
-1
0
0
0
0
Reactions
Visibility of the K ~ a)
(K±K~'//"~:)~'+~-
0.590
ol 0.196 ]N 1 h I 12
10
O O O ,¢+~.(KIKI~")
0.340
0.028 IN1ol k II 2
2
6±3
o o o ?r+~(K1K27r)
0.590
0
0 -+ 30
(K±K~ ~) ~+,-
0.590
+-
+1
1
0
+1
1
±1
-1
1
0
-1
1
-1
Production ratio Prediction
0
0.196 tN1ol k 1 t2
0.340
0
o o o 7f+Tr(K1K2?I)
0.590
0.098 IN~Ilkl12
(K±K1~ ) ~'+~-
0.590
{K°lK°ffr°) ? r + -
0.340
0.098 I k N 1112 1 o 0.028 I koNilo i2
(KIKI~")
0.340
0.085 I
(K~=KI~r~:) Ir+Tr-
0.590
0.098 IkiNlo 1 12
o o o "/T+y(KIK2~")
0.590
0.098 IkoNloI 12
o o ± 7r:Fffo (K1K2Tr)
0.340
0.042 I k l t 2 N b)
Nb)
c)
10 el
Experiment 10 ± 5
10 ± 5
0
6±3
5
0 -+ 30
10 c)
10 ± 5
6 c)
6+3
>/ 12 10 c)
>13
0 +- 02 10 ± 5 0t3 -0 0 +3 -0
a) We have taken account of the probability that the K~ decays into 7r+~r- and of the probability to see it in the bubble chamber.
b) N--
. 1 1 2I 1t2÷~ %
c) Normalization.
6KK
IKK K
lKI~
K
L~
Fig. 9. A representation of the KK~ system.
3.2. Spin and parity of the D ° The spin and the p a r i t y of the D ° have b e e n a n a l y z e d by studying both its p r o d u c t i o n and its d e c a y p r o p e r t i e s . F o r this a n a l y s i s a p u r i f i e d s a m p l e of D ° e v e n t s was used: m o r e p r e c i s e l y the events c o r r e s p o n d i n g to
706
C. D'ANDLAU et al.
1.62 < M 2 (I~Tr) -.< 1.74 GeV 2 f o r r e a c t i o n s (1)-(4) with the additional r e s t r i c t i o n t h a t the D ° is p r o d u c e d in a s s o c i a t i o n with an w o f o r r e a c t i o n (1) and a pO f o r r e a c t i o n s (2) and (4). T h e e v e n t s with 1.62 --< M 2 (K~K'41r "~) < 1.74 GeV 2 of the r e a c t i o n K~K~lra:~r°, s a t i s f y the additional r e s t r i c t i o n M2(K~IC~) --< 1.1 GeV 2. T h e s a m p l e s of e v e n t s u s e d f o r e a c h r e a c t i o n a r e : ~ p - ~ D ° o __. K~lK:eTr¥Tr~-TroTr±
42 e v e n t s ,
pp ~ D ° o --. K~iC41r~Tr¥Tr±
21 e v e n t s ,
pp--* D°(M) ~ K~K±Tr~(M)
36 e v e n t s ,
~p__., D ° o ~p ~ D°Tr°
..o..o o + r~lr~l~r ~r 7r ~ K~IC47r:~lr°
7 events, 16 e v e n t s .
With t h e s e r e s t r i c t e d s a m p l e s the b a c k g r o u n d d o e s not r e p r e s e n t m o r e than 20% of the e v e n t s . 3.2.1. Study of the D ° decay. Fig. 10 s h o w s the c h a r a c t e r i s t i c d i s t r i b u t i o n s of the D ° d e c a y . F i g s . 10b and 10c s h o w no c l e a r e v i d e n c e f o r a (KTr) o r a (KI~) r e s o n a n c e . But we should still t a k e a c c o u n t of the p o s s i b l e m a n i f e s t a t i o n of f i n a l - s t a t e i n t e r a c t i o n s b e t w e e n (Krr) o r (KK~. T h e P - w a v e (Klr) i n t e r a c t i o n is well known and can be p a r a m e t r i z e d by a K*(891) B r e i t - W i g n e r f o r m u l a . C o n c e r n i n g the KI~ t h r e s h o l d i n t e r a c t i o n , we know that it is c o r r e c t l y r e p r o d u c e d e i t h e r by a B r e i t - W i g n e r o r by a s c a t t e r i n g l e n g t h p a r a m e t r i z a t i o n (ref. [6]). T h e a c c u m u l a t i o n of e v e n t s at low KI~ m a s s v a l u e s l e a d s us to b e l i e v e t h a t lKI~ = 0 is d o m i n a n t . In this c a s e the spin and the p a r i t y of the D ° a r e g i v e n by:
gDo = LTr , PDO = ( -1)LTr+l , and when we r e s t r i c t o u r s e l v e s to take only the l o w e s t value of LTr, we have to c h o o s e f o r J ~ b e t w e e n 0 - , 1 + and 2-. T h e r e f o r e , to s t u d y the d e c a y of t h e D ° we t r y t h r e e h y p o t h e s e s , f o r which we give in appendix B the m a t r i x e l e m e n t s and in t a b l e 4 the r e s u l t s of fits p e r f o r m e d . F o r t h e s e fits we have u s e d the t h r e e d i s t r i b u t i o n s g i v e n by fig. 10b, c and d, and a l s o the p r o j e c t i o n s (Tlr/Trr)max and (TK~ - TK~)/TTrmax) of the D a l i t z plot p r e s e n t e d in ref. [2]. (i) If we a s s u m e that the p o p u l a t i o n of the d e c a y D a l i t z plot (fig. 10a) is g o v e r n e d by the p r o p e r t i e s of the d e c a y m a t r i x e l e m e n t a s d e t e r m i n e d m a i n l y by its t r a n s f o r m a t i o n p r o p e r t i e s r a t h e r than final s t a t e i n t e r a c t i o n s , then the h y p o t h e s i s JDPO = 0 - can be r u l e d out and JDPO = 1 + and 2- a r e equally probable ref.[2].
~p ANNIHILATION
(a) 0.64
OJ O
707
I
(c)
¢5
t9
c
0.56
I
Hv
Q48
.".,-:./. o°
•
.
:,L I
0.40
n
•
o °
O L.
2
E=
Z I
0.48
I
I
0.56
I
1.0
0.64
O C)~
25 20
:"
15
~.~ (b) ,,,,,, """ ..... "
-,°,~
~
E
~ z 0.5 M' (KTr)
0.6 GeV'
1.3
1.4
GeV a
(d)
Z 0.4
1.2
M' (KK)
M = ( K~' "n"+) G e V '
~'c0° ~I
I.I
M= ( K K ) ~< I.I GeV =
15
-I.0
0
1.0
Cos 8 K E
Fig. 10. Decay distributions for D ° events. The full lines drawn on the spectra are obtained from the fit described in the text.
(ii) If we s u p p o s e a s t r o n g P - w a v e (K~r) i n t e r a c t i o n , J P = O- and 2- a r e r u l e d out and only J P o = 1+ is c o m p a t i b l e with the decay of the D ° (table 4) (ref. [3]). (iii) A l t e r n a t i v e l y , if we i n t e r p r e t the o b s e r v e d population density of the Dalitz plot a s e s s e n t i a l l y being due to a s t r o n g S-wave i n t e r a c t i o n between the two K m e s o n s , and the KK i n t e r a c t i o n d e s c r i b e d e i t h e r by a B r e i t W i g n e r f o r m u l a (MKI~ = 1.02 GeV, F KK = 60 MeV) or by a s c a t t e r i n g length p a r a m e t r i z a t i o n with an a b s o l u t e s c a t t e r i n g - l e n g t h value l a t running f r o m 0.7 to 2.2 f m (ref. [6]) (table 4), 0- is the m o s t f a v o u r e d a s s i g n m e n t f o r D o, 2- is v e r y unlikely and 1 + is l e s s f a v o u r e d if tal > 1.5 f m .
Prob.
oL
1.0 ± 0.08
1.0 * 0.08
1.0 ~: 0.08
80%
43.6
Prob.
80%
43.6
2 X
80%
< l0 -4
107.3 41.8
3%
73.2
60%
2.10 - 4
93.8 42.5
40%
54.8
6%
0.28 ± 0.06
0.36 ± 0.08
0.76 ~ 0.15
< 10 - 4
161.8
2 X
52.9
48.1
38.7
Prob.
35%
55%
90%
< 10 - 4
3.10 - 4
89.8
211.5
< 10 - 4
< 10 - 4
157.1
120
54.3
2-
0.37 ± 0.03
0.42 ~ 0.03
0.53 • 0.04
N o t e s : (i) The e x p e c t e d v a l u e of t h e X 2 i s 58 f o r h y p o t h e s i s (1), (2), (3), (3') and 57 f o r h y p o t h e s i s (4). (ii) (KIK)S m e a n s a (KK) i n t e r a c t i o n r e p r o d u c e d by a B r e i t - W i g n e r f o r m u l a (MKI~ = 1.02 GeV, I"K~ = 60 MeV, s e e appendix C). (iii) (KI~)s L m e a n s a (KK) i n t e r a c t i o n d e s c r i b e d by a S - w a v e s c a t t e r i n g l e n g t h p a r a m e t r i z a t i o n ( s e e a p p e n d i c C).
X
60%
45.6
2.2 f m 2
60%
44.5
1.5 f m
60%
45.6
2.2 f m
(4) +(1- q) [D ° --, K891 + K]
60%
44.5
1.5 f m
1.5 x 10 - 3
1.5 × 10 - 3
88.8
0.7 f m
88.7
D °--* (KI~)SL +
(3')
65%
41.5
< 10 - 4
0.7 f m
D °--, (KK)s + 7r
C3)
367
71.7
< 10 - 4
310.8
a [DO--, (KK)s L + y]
* +K D °--, K891
L~"
D °--, KK +~"
(2)
(1)
1+
0
Table 4 Study of the D ° d e c a y .
>
>
~p ANNIHILATION
709
(iv) Finally we can suppose that the final state (KTr) and (KK~ i n t e r a c t i o n s a r e both p r e s e n t in the D ° decay. We a r e then led to p e r f o r m a fit with the following decay m a t r i x e l e m e n t s J~Pn = 0- , lJ~
i MO12 = alM°(K*)12 + ( l - a )
JDPo= 1+ ,
I Mll 2
I M°(KI~) 12 ,
= al~. Mi(K*)Mi(K*)I +(1-a)l $
.~
Mi(K~)Mi(KI~)I ,
$
tM212 = a l ~ M/J(K*) Mij(K*)I + (1-a) I~..MiJ(K~)Mij(KI~)I , ij ~J w h e r e the explicit e x p r e s s i o n s f o r MO(K*), M / (K*), M/J(K*), M°(KK), M i ( K ~ and M/J(KI~) a r e given in appendix B; then all the t h r e e hypotheses (table 4) (JP = 0-, 1 +, 2-) give good fits, we shall only e m p h a s i z e that the lowest a s s i g n m e n t (0-) is sufficient to r e p r o d u c e the e x p e r i m e n t a l r e s u l t s . JDPo = 2- ,
3.2.2. Orientation of the decay plane. The general f o r m a l i s m needed f o r this kind of study was given by B e r m a n and J a c o b [7]. In the c a s e of our e x p e r i m e n t , it allows one to p r e d i c t the f o r m of the distribution of the angle between the n o r m a l s to the decay (nd) and the production (np) planes of the D ° [W(cos 0nd.nn)], and also of the angle between n d and the line of flight of the D ° (D) defined in the ~p c.m. s y s t e m [ W ( c o s 0 n d . D ) ] . We give in appendix C the f o r m of t h e s e distributions for J ~ o = 0-, 1 ÷, 2-. Figs. 10a and 10b give the e x p e r i m e n t a l distributions forUall D ° events. T h e s e distributions a p p e a r to be i s o t r o p i c and do not allow us to distinguish between the different s p i n - p a r i t y h y p o t h e s e s for the D ° . But again one should note that the hypothesis JP = O- is sufficient to r e p r o d u c e them. ~ p .--I~ D° X °
40
(o)
(b)
O" E z
0 0
÷1 cos OND D
0
+1
cos ~ND.NP
Fig. 11. (a) Distribution of coSOBp .nd =rip .nd/(Inp[ [ndl) wherenp is the normal vector to the ~p production plane and Bd the normal vector to the decay plane of the D° . (b) Distribution of cos end./} =Bp .D/(IBpl ID~ w h e r e / ) is the vector characterizing of the line of flight of the DO.
710
C. D'ANDLAU et al.
4. CONCLUSION
In our study we have established a l m o s t without ambiguity the isospin (ID = 0) of the D °, and have shown that, for the c h a r g e conjugation, C D = +1 is favoured. For the spin and p a r i t y , the study of the decay and the production of the D ° does not f a v o u r any one of the t h r e e lowest spinp a r i t y a s s i g n m e n t s (0-, 1 +, 2-) compatible with the assumption lK~ = 0 suggested by the accumulation of the (KI~) m a s s e s at low values. However J P o = 0- is enough to r e p r o d u c e all the decay and production distributions, p~'ovided we take into account a s t r o n g (KK)I= 1 i n t e r a c t i o n at threshold, as seen in p a r t i c u l a r in ~p annihilations at r e s t in the t h r e e body channel KK~r.
APPENDIX A If we denote by k 0 and k 1 the amplitudes c o r r e s p o n d i n g to I(KK--) = 0 and I(KK~ = 1 r e s p e c t i v e l y , the decay amplitudes f o r the D into different obs e r v a b l e charge modes are: CD = +1, ID = 0: D ° =__kl [ ( K + K ~ -) - (K+K~Tr-) + ( K - K ~ "+) + ( K - K ~ "+) - (K+K-lr °)
4g
o
o o
1 {(K~K~ o) + ( K 2 K 2 ~ ) } ] .
CD = +1, ID = 1: D°
o o o ko [(K+K-Tro) _ 1 {(K~K~ITo) + (K2K2~)}]
+
-
1 o o:~ o o* D + = ~k o [(K+K-Tr +) --~{(K1K17T ) + (K2K2~)}]
+ ½k1 [(K=eK~Tro) $ (K~g~Iro) _ (K+K- r±) _ (K1K2~ r o o ~-)] . CD = -1, ID = 0: D ° =---~
_
(K+K- o)
o o o _ (K1K2~r)]
CD = -1, ID = 1: D ° = __k° [(K+K- o) _ (K1K2~O o o)] + ~k l l [(K+K~Tr-) _ ( K + K ~ -) - (K-K~
+) - ( K - K ~ . + ) ]
,
711
~p ANNIHILATION
- ½k1 [(K-~K~Tr°) ¥ (K'~K~Tr°) - (K+K-Tr+) 1
o o ±
V~ {(KIKI~ ) +
(K~I~+)}]
W e have seen that D is produced in association with a system X (co°, p, y, z;°), so we shall study final states of the form ~p ~ D ° X o . For ID = 0:
[DX>= N°°I D°X°> + N°II D°X° >. For ID = 1:
11
IDX> = ~i 0 ]D°X°>
No
+ (_N~o31 N11
iDoxO> Nlo1
) Io-x+>,
wnere' -Iv"Ipp ID' I x is the t r a n s i t i o n amplitude and ID, IX, Igp the isospin of the X s y s t e m and of the ~p s y s t e m . Of course the unique N/D' IX symbol l~p we use, depends on the charge conjugation and spin-parity assignment of the D together with the quantum n u m b e r s of the initial states.
APPENDIX B K K interaction:
-Mo(KK-) = 9
or BW(KI~) with ~9 = l + i a p1 ~ '
I~1 = 0"71 1.5 fm 2.2
or Bw( ) M _Ms2÷eMsrs M S = 1.02 GeV (ref. [5]) ,
_Mi(I¢~) = pi BW ( K ~ ,
F S = 60 M e V .
712
C. D'ANDLAU et al.
I
*"
p~ is the momentum of the ~ in the c.m. system of the D °. (K~')/=I interaction: Mo(K* ) = PK17r "PK2 BW (K~) +PK2~ "PK 1BW (K~.) , MiJ (K*)
=
i j [PK17r PK i
j
" Pk" 2 ~ 5 ij (PK17r .PK2) ] BW(K~) 2 +P3K17r -
j
i
2
""
*
+ [PK2~PK1 +PK27rPK 1 - ~ 5Z3(PK2~r"PK1)] BW(K 2) , i
,
M i (K*) = [ b Ei 1~ BW (K;) + PK27r BW (K2) ] ,
withPKm = momentum of K m in the c.m. system of the D, P K n ~ = momentum of Kn in the c.m. system of KnY, BW (I~) = M~m~
1 M 2 , + i M K , FK,
APPENDIX C
JDo o-
W (cOs0nd n p ) = ct , W(cos Ond.D)
= ct .
W (cos Ond.np ) = A 0 + A 1 cos 0 +A 2 cos 2 O ,
JDo= 1+t W(cos0nd.D )
= B O+B 2cos 20 .
i W(cos Ond.nP)=n~=O A o c o s n 0 , JDPo = 1- ~W(cos Ond.D ) = B0+B 2 cos20 + B 4 cos49 . We would like to thank Dr. S. Wojcicki for many stimulating discussions, and Professor Ch. Peyrou and Dr. R. Armenteros for their continuous support.
~p ANNIHILATION
713
REFERENCES [1] J. Barlow, E. Lillestdl; L. Montanet, L. Tallone-Lombardi, C. d'Andlau, A. Astier, L. Dobrzynski, S. Wojcieki, A.M. Adamson, J. Duboc, F. James, M. Goldberg, R.A. Donald, R.~lames, J. E. A. Lys and T. Nisar, Nuovo Cimento 5OA (1967) 701. [2] Ch. DTAndlau, A. Astier, M. Della-Negra, L. Dobrzynski, S. Wojcicki, J. Barlow, T. Jacobsen, L. Montanet, L. Tallone, M. Tomas, A.M. Adamson, M. Baubillier, J. Duboc, M. Goldberg, E. Levy, D.N. Edwards and J. E. A. Lys, Phys. Letters 17 (1965) 367. [3] D.H. Miller, Suh Urk Chung, Orin I. Dahl, R.I. Hess, L.M. Hardy, J. Kirz and W. Koellner, Phys. Rev. Letters 14 (1965) 1074. [4] J. Duboc, A. Minten and S. Wojcicki, CERN Report 65-2. [5] A. Rosenfeld, A. B a r b a r o - G a l t i e r i , W. Podolsky, L.R. P r i c e , P. Soding, Ch. Wohl, M. Roos and W. Willis, Revs. Mod. Phys. 39 (1967) 1. [6] A. Astier, J. Cohen-Ganouna, M. Della-Negra, B. Marechal, L. Montanet, M. Tomas, M. Baubillier and J. Duboc, Phys. Letters 25B (1967) 294. [7] S. M. Berman and M. Jacob, Phys. Rev. 139B (1965) 1023.